#include<bits/stdc++.h>
using namespace std;
#define sp <<' '<<
#define se second
#define fi first
#define pb push_back
#define FOR(i,a) for(int i=0;i<(a);i++)
#define FORE(i,a,b) for(int i=(a);i<(b);i++)
#define DEBUG(x) cout<<#x sp x<<endl
#define mid (l+r)/2
typedef vector<int> vi;
typedef pair<int,int> pii;
typedef vector<pii> vii;
const int MAXN=2e5+5;
int n,k;
vi a;
int p[MAXN], dep[MAXN], tin[MAXN], tout[MAXN];
vi adj[MAXN], renk[MAXN];
map<int,int> cocuk[MAXN];
pii ans;
int f,timer;
void merge(int nd,int kom){
if(cocuk[nd].size()<cocuk[kom].size()) cocuk[nd].swap(cocuk[kom]);
for(auto el:cocuk[kom]) cocuk[nd][el.fi]+=el.se;
}
void dfs(int nd,int ata,int h){
if(f==0){
tin[nd]=timer++;
dep[nd]=h;
}
else{
cocuk[nd][dep[nd]]++;
}
for(auto kom:adj[nd]){
if(kom==ata) continue;
dfs(kom,nd,h+1);
if(f) merge(nd,kom);
}
if(f==0){
tout[nd]=timer++;
}
else{
pii res={0,0};
map<int,int> mp;
for(auto el:renk[a[nd]]){
if(tin[nd]<tin[el] and tout[el]<tout[nd]){
res.fi++;
mp[dep[el]]++;
}
}
for(auto el:renk[a[nd]]){
if(tin[nd]<tin[el] and tout[el]<tout[nd]) continue;
if(cocuk[nd][dep[el]]-mp[dep[el]]>0){
res.fi++;
res.se++;
mp[dep[el]]++;
}
}
if(ans.fi<res.fi) ans=res;
if(ans.fi==res.fi and ans.se>res.se) ans=res;
}
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(0);cout.tie(0);
cin>>n>>k;
a.resize(n+1);
FORE(i,1,n+1){
cin>>a[i];
a[i]++;
renk[a[i]].pb(i);
}
FORE(i,2,n+1){
cin>>p[i];
p[i]++;
adj[p[i]].pb(i);
}
timer=1;
dfs(1,-1,0);
f=1;
dfs(1,-1,0);
cout<<ans.fi sp ans.se-1<<endl;
}
